Give a convex function \(f(\cdot , )\) , we consider empirical risk minimization on a dataset of \(n\)  points.
We assume \(f(\cdot , )\)  is 1-Lipschitz for all \(\) , and diam\(() \le 1\) . This is only for simplification as the bounds scale naturally with these constants, as discussed in [1]}. We look at algorithms, which given two datasets \(S\)  and \(S^{\prime }\)  of size \(n\)  differing by one point, disagree only on a set of measure at most an \(\rho \) .
